Question

# The amount of pollution content added in air in a city to $$x$$ diesel vehicles is given by $$P(x) = 0.005x^3+0.02x^2+30x$$. Find the marginal increase in pollution content when $$3$$ diesel vehicles are added.

Solution

## $$P(x)=0.005x^3+0.02x^2+30x$$Differentiating w.r.t to x we get,$$P'(x)=3(0.005)x^2+2(0.02)x+30$$$$P'(3)=3\times 0.005(3)^2+2(0.02)(3)+30$$$$P'(3)=30.255$$Maths

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